2Learning Objectives Recap properties of α, β, γ radiation. Describe and explain the relative hazards to humans when exposed to α, β, γ radiation.Recap the inverse square law of radiation.Describe how this applies to the safe handling of radioactive sources.
3Quick RecapComplete the table (in pencil) that describes the properties of the three common radiations:-RadiationParticleRange in airStopped By
4Recap - Answers Radiation Particle Range in air Stopped By Alpha Helium nucleus (P)Few mm (P)Paper (P)BetaHigh speed electron (P)Few cm (P)Aluminium sheet (P)GammaEnergetic photon (P)Infinite (P)Several cm lead (P)
5Ionisation What is ionisation? Which do you think is the most ionising?
6Ionisationα - Intense, ionises about 10,000 atoms per alpha particle. (because strongly +ve and large)β - Less intense than a, about 100 ionisations per particle. (because lower charge, but higher speed)γ - Weak interaction about 1 ionisation per mm.
7Hazards α – Once it gets in it is highly damaging to body tissue. Luckily can’t pass through skin but could be inhaled or ingested. Considered less damaging than gamma rays or alpha particles.β – Lower interaction rate means it is much less damaging to body tissue than alpha. Used as medical tracers.γ - can be a dangerous form of radiation, as they are very penetrating. Needs intense or prolonged radiation to cause damage to cells.
8Annoying Question (10 mins) Explain the dangers associated with radioactive sources (8 marks).Write a mark scheme for this question i.e. assign 1 mark each to 8 short but relevant statements.
9Possible Mark Scheme Alpha is intensely ionising. Although short range and kept out by skinIngestion of alpha emitters can do immense damage to the cells.Beta is less ionisingBut can penetrate the bodyGamma is highly penetratingBut causes little ionisation.Long term exposure leads to damage to DNA
10Spare QuestionAlpha and beta particles lose about 5 × J of kinetic energy in each collision they make with an air molecule. An alpha particle makes about 105 collisions per cm with air molecules, while a beta particle makes about 103 collisions. What is the range of an alpha particle and a beta particle if both start off with an energy of 4.8 × J?
11Spare Question AnswerBoth particles lose all their energy in 4.8 × J ÷ 5 × J (P) = collisions (P) The alpha particle has a range of ÷ 105 cm-1 = 0.96 cm (P) The beta particle has a range of ÷ 1000 cm-1 = 96 cm. (P)
12Inverse Square Law for γ When taking a reading of intensity, I, at a distance x from the source, I0 is the intensity at the source and k is a constant.Intensity (number of photons per unit area) decreases by the square of the distance.So doubling distance from source means only a quarter of radiation reaches you – so keep them at a distance! -tongsCan be written as:-or:-
13Learning Objectives Recap properties of α, β, γ radiation. Describe and explain the relative hazards to humans when exposed to α, β, γ radiation.Recap the inverse square law of radiation.Describe how this applies to the safe handling of radioactive sources.
15HomeworkResearch and explain how electron diffraction can be used to determine the radius of the nucleus (6 Marks)Past Paper Question on today’s material.Complete both by Next Lesson, next Monday, Period 5.
16Learning ObjectivesState and use the equation for dependence of radius on nucleon number.Calculate nuclear density.Recall the implications of the high nuclear density compared to atomic density.
17Equation Dependence of radius on nucleon number:- [The term A1/3 means the cube root of A, the nucleon number. The term r0 is a constant with the value 1.4 × m. R is the nuclear radius.] What physical quantity is r0?Rearrange in the form of A=.Try working out R for Gold (A =197 ) and Carbon (A=12)
18Nuclear Density Radius of a carbon nucleus ~ 3.2 x 10-15m. Radius of a gold nucleus ~ 8.1 x 10-15m.Mass of a carbon nucleus ~ 2.00 x 10-26kg.Mass of a gold nucleus ~ 3.27 x 10-25kg.What are the densities of the nuclei?
19Nuclear Density Density of carbon nucleus ~ 1.46 x 1017 kg m-3. Density of gold nucleus ~ 1.47 x 1017 kg m-3.Very high! One teaspoon = 500 million tonnes.So pretty much the same, regardless of element.Ext: Work out mass of neutron star based on this density. How does it compare to solar mass?
20Nuclear Density Nuclear density >> Atomic Density This implies:- Most of an atom’s mass is in its nucleus.The nucleus is small compared to the atom.An atom must contain a lot of empty space.
21Example Exam Questions (a)If a carbon nucleus containing 12 nucleons has a radius of 3.2 x 10-15m, what is r0?(b) Calculate the radius of a radium nucleus containing 226 nucleons.(c) Calculate the density of a radium nucleus if its mass is 3.75 x kg.Q2: A sample of pure gold has a density of kg m-3. If the density of the gold nucleus is 1.47 x 1017kg m-3 discuss what this implies about the structure of a gold atom.
22Learning ObjectivesState and use the equation for dependence of radius on nucleon number.Calculate nuclear density.Recall the implications of the high nuclear density compared to atomic density.
24HomeworkWhy are spent fuel rods more radioactive after removal from the reactor?What are the different types of radioactive waste?How is each type stored/disposed?
25Filling the Gapsγ emitters can indeed be used as medical tracers as we thought.Cell membranes can also be destroyed as well as affecting DNA.
26Learning ObjectivesExplain how an estimate for the nuclear radius can be obtained from Rutherford’s Experiment.
27Rutherford’s Alpha Scattering At P, the point of closest approach, all of the initial kinetic energy of the alpha is converted to electrostatic potential energy.
28Electrostatic Potential Energy The equation for Electrostatic Potential Energy is given by this equation:-Where:-EP is the Electrostatic Potential Energyrc is the distance of closest approachε0 is the permittivity of free space (constant - see data booklet)Q1Q2 are the charges of the two particles involved.
29Little bit of Maths… Solving to find rC, what do we get? Rearranging… Remember:Q1=2e = 2 × 1.60 × C (α is He nucleus)Q2=79e = 79 × 1.60 × C (79 protons in Gold nucleus)EP=7.68 MeV = 768 × 106 × 1.60 × J (K.E. of α particles fired at the foil.)ε0 = 8.85 × Fm-1 (from the data booklet)rc= 2.96 × m (a bit large)
30A couple of points…The nucleus is treated as a point charge. At this level it is not.The alpha particles are stopped some distance away from the nucleus.It takes higher energy alpha particles to penetrate the nucleus.The values for the nuclear radius given by other particles such as protons, neutrons and electrons are slightly different.…so really it is only an upper limit on the nuclear radius.
31Method 2 About 1 in 10,000 particles are deflected by more than 90º. For a thin foil (so that only one scattering) with n layers of atoms, the probability of being deflected is about 1 in 10,000n.This probability depends on effective cross section of nucleus to the atom:-Typically n=10,000 so d = D/10,000
32QuestionsA) For a metal foil which has layers of atoms, explain why the probability of an α particle being deflected by a given atom is therefore about 1 in 10,000n. (assume 1 in deflected by more than 90º)B) Assuming this probability is equal to the ratio of cross sectional area of the nucleus to that of the atom, estimate the diameter of a nucleus for atoms of diameter 0.5 nm in a metal foil of thickness 10 μm.
34Physics Workshop Every Wednesday 3.40pm-4.40pm in O8 Is this time good for most people?
35Learning ObjectivesDescribe the range of safety features associated with a nuclear reactor.Derive the equation relating half life and the decay constant.Practice calculations on radioactive decay.
36High Energy Electron Diffraction Any 6 from:-A beam of high energy electrons is directed at a thin sheet of an elementand accelerated through a potential difference of about 108 volts (MeV/high energy)A detector measures the number of electrons diffracted at a number of different angles.Scattering effects occur due the charge of the nuclei and electron and this causes the count rate of the beam of electrons to decrease as angle increases.The electrons are also diffracted by the nuclei in the sheet which causes minima and maxima to observed in the final patternas long the de Broglie wavelength of the electrons is of the same order as the size of the nucleus, which is about m.The diameter of the nucleus can be calculated using the angle to the first minimum, θminand the wavelength of the incoming beam λ using the diffraction equation R sin θmin = 0.61λ.
37Safety FeaturesThe reactor is a thick steel vessel designed to withstand the high pressure and temperature in the core.The core is in a building with very thick concrete walls which absorb the neutrons and gamma radiationEmergency shut down system – designed to insert the control rods fully into the core.Sealed fuel rods are inserted and removed using remote handling devices.Spent rods are more radioactive than before use.
38How to Remember? C - Concrete building. R - Remote Handling. E - Emergency shut down system.S - Steel vessel for reactor core.S - Spent fuel rods much more radioactive.Spells CRESS, helps us remember?
39Dangers of Nuclear Power Chernobyl (1986)Wanted to see if coolant pumps would keep operating if there was a loss of power.When they pushed control rods into reactor, caused loss of power and reversed direction of the rods!
40AftermathOverheating caused decomposition of water into hydrogen and oxygen which gases collected at the top of the vessel.Ignited and blew the lid off the reactor and turned the vessel on its side.Nine tonnes of caesium-137 floated across Europe along with many other tons of radioactive material.Caesium-137 is water-soluble and extremely toxic in minute amounts (half life 30 years).
41Okay let’s try itDescribe the range of safety features associated with a nuclear reactor (5 marks).
43Learning Objectives Define specific heat capacity Perform calculations using ∆Q=mc ∆θDescribe how specific heat capacity can be measured in the lab
44HomeworkComplete worksheet to practice calculations we will look at today.
45Why do we careThe anomalously large SHC of water is particularly important for the development and maintenance of life on Earth.
46Why are we learning this? Historical ContextImages of Joule, KelvinSteam enginesThermal physics in stars
47Which is hotter. Bath water or a lit match Which is hotter? Bath water or a lit match? Which needed more energy to heat it?
48Heat vs. Temperature Heat as water and temperature as wetness analogy ‘Heat’ is not an entity but a short hand name for a process (heating as oppose to working).
49State vs. PhaseSolids, liquids and gases are three of the different phases of matter (superfluids and plasmas are two others. Thus melting, boiling etc are changes of phase.Each phase can exist in a variety of states depending upon e.g. the temperature and pressure.
50Specific Heat Capacity Definition:-The specific heat capacity (c) of a substance is the amount of energy needed to raise the temperature of 1kg of the substance by 1K (or 1 ºC)
51Specific Heat Capacity Equation:where:-∆Q is the energy change in Jm is the mass in kgc is the specific heat capacity in J K-1 kg-1∆θ is the temperature change in K
52Worked Example 1A bucket containing 11.5 litres of cold water at 10°C is taken into a house at a warmer temperature and left inside until it has reached thermal equilibrium with it new surroundings.If 504 kJ of energy is absorbed from the surroundings to heat the water, what is the temperature of the room?∆Q =504 kJm=11.5 kgc = 4200 J kg-1 °C-1∆θ = ?Using∆ θ = 504,000 J / (11.5kg × 4200 J K-1 °C-1 ) = 10.4 °C (to 3 s.f.)So temperature of the water = 10°C °C = 20.4 °CTemperature of the room = T of water in thermal eqm. = 20.4 °C
53Worked Example 2A 60 W immersion heater takes 2.5 minutes to heat 0.5 kg of water from 21 to 25, what is the specific heat capacity of the water.P = 60 W∆ t = 2.5 minutes = (2.5 × 60)s = 150 s∆θ = θ2 - θ1 = 4 oC = 4 Km=0.5 kgc =?∆Q = P ∆ t = 60 W × 150 s = 9,000 Jc = 9,000 J / (0.5 kg × 4 K) = 4,500 J kg-1 K-1Why is it higher than the accepted value of c = 4200 J kg-1 K-1?
54NoteIf a question includes heating and then melting a substance then use:-
55Learning Objectives Define specific latent heat Perform calculations using ∆Q=mlDescribe how specific latent heat of fusion/vaporisation can be measured in the labExplain why energy is needed to evaporate a liquid/melt a solid
56SafetyStudents must not sit down to watch this experiment - serious scalding has occurred when the beaker breaks or falls and the pupil has been unable to move away instantly.
57Demonstration What tells you the water is boiling? So energy is being supplied but the temperature is not rising?What is going on?Work is being done to separate the particles against intermolecular attractive forces.
59s.h.c vs. latent heat (simple terms) Specific Heat CapacityEnergy needed to heat somethingLatent HeatEnergy needed to change phase
60DefinitionThe specific latent heat (l) of fusion or vaporisation is the quantity of thermal energy required to change the state of 1kg of a substance.Fusion (liquid solid)Vaporisation (liquid gas)…or the other way (Melting/Condensing)
61Equation where:- ∆Q is the energy change in J m is the mass of substance changing phase in kglv is the latent heat of vaporisation in J kg-1lf is the latent heat of fusion in J kg-1
62Worked Example 1The specific latent heat of fusion (melting) of ice is 330,000 J kg-1. What is the energy needed to melt 0.65 kg of ice?∆Q = ml = 0.65 kg × 330,000 J kg-1 = 210,000 J (2 s.f.)
63(resourcefulphysics.org) Worked Example 2The power of the immersion heater in the diagram is 60 W. In 5 minutes, the top pan balance reading falls from 282g to 274g. What is the specific latent heat of vaporisation of water?P = 60 W∆ t = 5 minutes = (5 × 60)s = 300 sm = m2 - m1 = 282g – 274g = 8g = kglv = ?∆Q = P∆ t = 60 W × 300s = 18,000 Jlv = ∆Q/m = 18,000 J / kg = 2.3 × 106 J kg-1 (2 s.f.)(resourcefulphysics.org)
64Gas Laws & Absolute Zero Thermal Physics Lesson 3
65Learning ObjectivesState the three gas laws, describing the relationships between p,V,T and massDescribe how the thermodynamic scale is defined.Define absolute zero.Convert temperatures between Celsius and Kelvin.
66Thermodynamic Temperature Scale A change of 1 K equals a change of 1 oC.To convert from degrees Celcius into kelvin add :-
67DefinitionAbsolute Zero is the lowest possible temperature, and something at this temperature has the lowest possible internal energy.This is zero kelvin, written 0 K, on the thermodynamic temperature scale.
68Boyle’s Law Temperature and moles of gas are constant Graph is hyperbolic (see below) and asymptotic to both axesPressure and volume are inversely proportional to each other
69Ideal Gas vs. Perfect Gas Strictly speaking an ideal gas is one that obeys Boyle’s law with complete precision. A perfect gas is a real gas under conditions that Boyle’s law is a valid enough description of its behaviour.
70Charles’ Law Pressure and moles of gas are constant Graph is linear (see right)Volume and temperature are directly proportional to each other
71Pressure Law (Gay-Lussac's Law ) Volume and moles of gas are constantGraph is linear (see right)Pressure and temperature are directly proportional to each other
72Avogadro’s LawThe most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. This means that the constant is given by:-
73Avogadro’s ConstantOne mole of any gas contains the same number of particles. This number is called Avogadro’s constant and has the symbol NA. The value of is 6.02 × 1023 particles per mole.
74Ideal Gas Equation/Molar & Molecular Mass Thermal Physics Lesson 5
75Learning ObjectivesPerform calculations using the ideal gas equation pV=nRTDescribe the conditions for which a real gas behaves like an ideal gasDefine a moleCalculate the number of moles in a gas using N=nNA
76The Ideal Gas EquationCombining the three gas laws gives the equation:-The constant is equal to nR.Works well for gases at low pressure and fairly high temperatures
77Equation of StateRecall that each phase can exist in a variety of states e.g. the temperature and pressureThus the Ideal Gas Equation of StatepV = nRT summarises the physically possible combinations of p, V and T for n moles of the ideal gas.
79Learning ObjectivesExplain the increase of pressure of a gas when it is compressed or heated.Describe the distribution of molecular speeds.Derive the kinetic theory equation.
80Explaining the gas laws Assume a gas consists of point molecules moving about at random, continually colliding with the container walls.Each collision causes a force on the container and it is the force of these many impacts that causes the pressure of the gas on the walls.
81Explaining the gas laws Boyle’s Law – reducing volume means less distance between collisions with the walls so more collisions per second.Pressure Law- raising the temperature increases the average speed of the molecules so more frequent and harder impacts with the walls.
82Molecular Speeds The molecules in a gas have a range of speeds. The root mean square speed, crms, of the molecules is given by:-Where N is the number of molecules in the gas and c1,c2 are the speeds of molecules 1,2, and so on.Note that this is not the same as mean speed.
84The Kinetic Theory Equation For an ideal gas consisting of N identical molecules, each of mass m, in a container of volume V, the pressure p of the gas is given by:-Where crms is the root mean square speed of the gas molecules.This is the equation we are going to derive.
85First, some assumptions Volume of the molecules negligible compared with volume of the gas.They do not attract each other.They move in continual random motion.The collisions are elastic collisions (no loss of k.e.)Duration of collisions much shorter than time between collisions.
86Remembering Assumptions R - Random motion.A – Do not Attract each other.V - Volume of the molecules is negligibleE - Elastic collisionsD - Duration of collisionsSpells - RAVED
87Here we go…We consider a molecule of mass m in a box of dimensions lx, ly and lz with a velocity components u1, v1 and w1 in the x, y and z directions respectively.
88A derivation of two halves… The strategy is to derive the pressure for one molecule on one face (1st half) and then sum all the pressures from all the molecules (2nd half).The first part involves Newton’s second law which states that the force on a body is equal to the rate of change of momentum.
89Also note… The speed c of the molecule is given by:- This comes from doing Pythagoras’ theorem in 3 dimensions.We will use this later in the 2nd half
90Find the force on one molecule… When the molecule impacts with Face A the x-component of its momentum is changed from mu1 to -mu1.But we want the rate of change of momentum, so need to divide by the time taken between collisions with Face A.
91Time, t, between collisions… So Newton’s 2nd Law gives us:-And Newton’s 3rd Law gives us:-
92Pressure Recall that to work out the pressure:- So the pressure p1 on face A:-So that’s the first bit done! – the pressure from one molecule in one direction.
93Summing the pressuresThe total pressure on face A can be calculated by summing the pressures of all of the molecules:-Where p2, p3… refer to the pressures of all the other molecules up to N molecules.
94Summing the pressures The last line can be rewritten as:- Where the mean square x-component velocity is given by:-And similar equations can be derived for the y and z components
95Almost there…But we want our equation to include the root mean square speed in all directions. Using Pythagoras’s theorem, the speed for one molecule is given by:-You can show that the root mean square speed for all the molecules is:-
96Almost there… Because the motions are random we can write:- Otherwise there would be a drift of particles in one direction. So using the above two equations:-So now we can write:-
97Final Rearrangement The Kinetic Theory Equation:- Can also be re-written as:-Because:-
98Recap Use Newton’s Second Law Use Newton’s Third Law Calculate pressure due to one molecule (force/area)Sum the pressures of all the molecules.Rewrite the speed in terms of root mean square speed.
99Kinetic theory applets There are a number of simulations on the internet. You will need to pick those that suit your specification and needs. Some suggestions are below: -The following were operational in October 2005Boyle’s LawEffect of temperature and volume:Distribution of velocity:Molecular Model of an ideal gas:
100Deriving Ideal Gas Equation From Boyle’s Law:From Pressure Law:From Avogadro’s Law:Combining these three:Rewriting using the gas constant R:Therefore:-
101Mean kinetic energyThe mean kinetic energy of a molecule is the total kinetic energy of all the molecules/total number of molecules.The root mean square speed is defined as:…and so the mean kinetic energy of one molecule is gvien by…
102Mean Kinetic EnergyNote we have two equations with pV on the left hand side.(N=nNA)The Boltzmann constant, k, is defined as R/NA.
103Mean Kinetic Energy Multiply both sides by 3/2. Mean kinetic energy of a molecule of an ideal gas.Kinetic energy of one mole of gas(because R=NAk)Kinetic energy of n moles of gas.
105HomeworkFinish the past paper questions by next Friday (October 16th).
106Learning ObjectivesDescribe evidence supporting the kinetic theory of gases.
107Robert Brown ( )In 1827, the botanist Robert Brown was looking at pollen grains in water.He noticed that they constantly moved with a zigzag random motion.
108Brownian Motion Experiment We can observe Brownian motion in the lab.We put smoke in a brightly lit glass jar and observe the particles using a microscope.Observe bright specks moving haphazardly from side to side and up and down.
109Brown couldn’t explain it… Einstein used it 80 years later as evidence for the existence of molecules in the air.The randomly moving molecules were hitting the smoke particles unevenly, causing the motion.